Wick quantisation of a symplectic manifold
High Energy Physics - Theory
2009-11-07 v1
Abstract
The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on the manifold. The cohomological obstruction is identified to the equivalence between the Wick star-product and the Fedosov one. In particular in the K\"ahler case, the Wick star-product is shown to be equivalent the Weyl one, iff the manifold is a Calabi-Yau one.
Keywords
Cite
@article{arxiv.hep-th/0103091,
title = {Wick quantisation of a symplectic manifold},
author = {V. A. Dolgushev and S. L. Lyakhovich and A. A. Sharapov},
journal= {arXiv preprint arXiv:hep-th/0103091},
year = {2009}
}
Comments
Talk given at the International Conference ``Supersymmetry and Quantum Field Theory'' (Kharkov, July 25-29, 2000), dedicated to the memory of Professor D.V. Volkov. To be published in Nuclear Physics B Conference Supplements